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'Enclosing Squares' printed from http://nrich.maths.org/

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Here's a problem to work at with your graphic calculator or graph-plotting package on a computer.

If you plot the following lines

$\begin{eqnarray} y &=& 2x + 1\\ y &=& 2x + 4 \\ y &=& -0.5x + 1\\ y &=& -0.5x + 2.5 \end{eqnarray}$

the lines will enclose a square.

Can you find other sets of sloping lines that enclose a square?

If you are given the equations of two parallel lines

$y = ax + b$ and $y = ax + c$

can you explain how to find the equations of the other two lines that would enclose a square, if you know that one of the vertices is at $(0,b)$?

[In the example at the top, $a = 2$, $b = 1$ and $c = 4$]